Transcript drburts_physics_notes

PHS 116
Chapter 4 – Gravity,
Projectiles, Satellites
Activity 1
[Gravity and reaction time]
Sir Isaac Newton
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Did not “discover”
gravity
First to realize that
gravity is not
confined to Earth
Forces must act on
the planets
Netwonian synthesis
4.1 Universal Law
of Gravity
Newton: The moon
“falls” away from
straight line
motion
Law of Universal Gravitation
After observing Halley’s comet
 Came up with this relationship
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F
~
mass1 x mass2
(distance)2
The Universal Gravitational
Constant (G)
F~
mass1 x mass2
(distance)2
F = G mass1 x mass2
(distance)2
G = 6.67 x 10-11 N m2/kg2
That’s 0.0000000000667
Henry
Cavendish
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First to
calculate “G”
independently
G = __F___
(m1m2/d2)
Sample Problem: Use “G” to
calculate the mass of the Earth!
Assume you have a 1 kg mass.
F = 9.8 N (we round to 10 usually)
G = 6.67 x 10-11 N m2/kg2
m2 = 1 kg
d = Earth’s radius = 6.4 x 106 m
[on board]
4.2 Effect of Distance on Gravity
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Gravity is weak to begin with
 weakest
of the four fundamental forces
 gravity, electromagnetic, weak & strong
nuclear forces
As distance increases, gravity falls off by
1/d2
 Similar example: spray paint
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9
1/9
16
1/16
Worksheet
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page 27
Distance
Refers to the distance between the “center
of mass” for the two objects
 The greater an object’s distance from the
weighs
Earth, the less it __________
 The force of attraction approaches zero at
very large distances, but can never reach
zero
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Question
You climb up a tree 4 m high and measure
the force of gravity on your body.
 You then climb up a tree 8 m high and
measure the force of gravity on your body.
 Do you weigh 4 times less (1/d2) when
you’re up the 8 m tree?
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4.3 Weight and
Weightlessness
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Weight has no
meaning without the
concept of “support
force”
When you take away
the support force you
are “weightless” or in
“freefall”
Weight
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You only weigh
as much as the
amount of
support force
you feel
Weightlessness
Artificial Gravity
http://www.youtube.com/watch?v=J0bnL3Hyf
Uo
4.4 Universal Gravitation
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Why are the planets round?
mass contained in the planet exerts gravity
on other mass within the planet
a sphere is the best way to distribute gravity
equally
[draw on board]
Planetary Perturbations
Planets influence other planet’s orbits
http://www.youtube.com/watch?v=zJACUydNL8
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F = G mass1 x mass2
(distance)2
J. Locke 1632 - 1704
Worksheet
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page 28
4.5 Projectile Motion
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Gravity causes the path of projectiles thrown
horizontally to curve
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To analyze properly, look at horizontal and
vertical components of motion separately
The horizontal component
Object moves at
constant velocity, no
acceleration, due to its
own inertia
 if we ignore air
resistance
dhorizontal = velocity x time
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The vertical component

acceleration due to
gravity
dvertical = ½ g t2
Combined
Projectiles
Launched
Horizontally
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The curved path is
called a parabola
Follows parabolic
motion
Object will hit the
ground at the same
time an object
dropped straight down
will hit
Projectiles
Launched at an
Angle Up
Still follows
parabolic motion
 Object will hit the
ground after object
dropped straight
down
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Projectiles
Launched at an
Angle Down
Still follows
parabolic motion
 Object will hit the
ground ______
the same object
dropped straight
down?
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Worksheet
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page 29, 30
dideal - dparabola = ½ g t2 = 5 t2
Launching Projectiles
What trends do you notice?
 What’s the ideal launch angle?
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What other effects?
air resistance (lower angle = less air
resistance)
 Spin for golf balls (lower angle = less spin)
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Time of Flight
deceleration of g =
acceleration of g
 time up = time
down
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Worksheet
pages 31, 32
4.6 Satellites
The earth is not flat
 If an object is projected fast enough, it can
“fall” all the way around the earth
 satellites
 18,000 mph for a baseball
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The Moon
a projectile that circles the Earth
 definitely influenced by Earth’s gravity, as
are other satellites
 Has enough velocity not to fall into the
Earth (or it would’ve done so long ago)
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4.7 Circular Orbits
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A satellite in orbit always moves in a direction
perpendicular to the force of gravity acting on it
A very special form of free fall (no support force)
The higher the orbit, the less the speed, the
longer the path, and the longer the period (time
it takes to make one orbit)
8 km/s ensures a perfect circular orbit
above atmosphere
4.8 Elliptical Orbits
If a projectile exceeds 8 km/s
 orbit will be an ellipse
 speed is not constant around the ellipse
 faster nearer massive object
 highest P.E. farthest from massive object
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PE = mgh
KE = ½ mv2
W =F x d
Worksheets
pages 33-35
4.9 Escape Velocity
Fire an object vertically
 What normally happens?
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Escape Speed
The “initial burst” speed required to
escape orbit
 11.2 km/s for Earth (~25,000 mph)
 Leaves Earth, traveling slower and slower
 From any planet (or body):
v = (2 G M / d)1/2
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Escape Speeds
Sun
Jupiter
Earth
Mars
Moon
333,000 Earth
318 Earth
1 Earth
0.11 Earth
0.0123 Earth
620 km/s
60.2 km/s
11.2 km/s
5.0 km/s
2.4 km/s
Escape Speed
Only pertains to the initial
thrust needed
 Rockets could burn out if
initially 11.2 km/s
 You can actually escape
at any speed if you’re
willing to take enough
time to do it
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Chapter 4 Homework
Exercises: 1, 2, 5, 6, 9, 12, 13, 20, 22, 27,
30, 32, 36, 37, 40, 49
Problems: 1, 2, 3, 8